Prove the radius of the incircle of an equilateral triangle is half the radius of its circumcircle.

In the picture below, a triangle is formed by a tangent to a circle, the radius through the point of contact and a line through the center. Draw this in your notebook.

In the picture below, a triangle is formed by a tangent to a circle, the radius through the point of contact and a line through the centre. Draw this in your notebook.

In the picture, all sides of a rhombus are tangents to a circle. Draw this picture in your notebook.

Prove that the tangents drawn to a circle at the two ends of a diameter are parallel.

What sort of a quadrilateral is formed by the tangents at the ends of two perpendicular diameters of a circle?

What is the connection of tangent with the line touching a circle?

Draw a circle of radius $2.5$ centimetres. Draw a triangle of angles $40°, 80°, 60°$ with all its sides touching the circle.

In the picture, the small triangle is equilateral. The sides of the large triangle are tangents to the circumcircle of the small triangle at its vertices.
Prove that the large triangle is also equilateral and its sides are double those of the small triangle.